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In the following figure, If BC = 8 cm, AB = 6 cm, AC 9 cm, then DC is equal to :
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- 7 cm
- 4.8 cm
- 7.2 cm
- 4.5 cm
- None of these
Correct Option: B
From above given figure , BC = 8 cm, AB = 6 cm and AC 9 cm
Using the sine fomula, we have
| = | = | |||
| sinA | sinB | sinC |
| ∴ | sin40° | = | sin(40°+C) |
| BD | 6 |
| ⇒ | sin40° | = | sin[180-(40°+C)] | = | sin(140 - C)] | ............. ( ⅰ ) |
| B - DC | 6 | 6 |
| Also , | sin40° | = | sin(140 - C)] | ............. ( ⅱ ) |
| DC | 9 |
∴ From (i) and (ii) given
| = | 9 | = | 3 | ||
| 8 - DC | 6 | 2 |
⇒ 2DC = 24 - 3DC ⇒ 5DC = 24
| ⇒ DC = | 24 | ⇒ DC = 4.8 |
| 5 |
